Question

You receive a sample in your lab. You are tasked to date the sample using radiocarbon dating. The sample is expected to have 0.005 g of Carbon-14. It currently has 0.002 g of Carbon-14. How old is the sample? (Hint; The half-life of Carbon-14 is 5,730 years)

Answer 1

Explanation:

To determine the age of the sample using radiocarbon dating, we can use the concept of half-life. The half-life of Carbon-14 is 5,730 years, meaning that after 5,730 years, half of the original Carbon-14 in a sample will have decayed.

Given that the sample currently has 0.002 g of Carbon-14 and started with 0.005 g, we can calculate the number of half-lives the sample has undergone.

First, let's determine the fraction of Carbon-14 remaining in the sample:

Fraction remaining = (Amount remaining) / (Original amount)

Fraction remaining = 0.002 g / 0.005 g = 0.4

Next, we need to calculate the number of half-lives the sample has undergone:

Number of half-lives = ln(Fraction remaining) / ln(0.5)

Number of half-lives = ln(0.4) / ln(0.5)

Number of half-lives ≈ 0.916 / -0.693 (using natural logarithm values)

Number of half-lives ≈ -1.32

Since the number of half-lives is negative, we need to take its absolute value. The absolute value of -1.32 is 1.32.

The age of the sample can now be calculated by multiplying the number of half-lives by the half-life of Carbon-14:

Age = Number of half-lives * Half-life

Age = 1.32 * 5,730 years

Therefore, the age of the sample is approximately 7,557.6 years.

Answer 2

Half of the initial Carbon-14 remains, indicating one half-life passed. Since its half-life is 5,730 years, the sample is roughly 5,730 years old.

Determining the Sample's Age through Carbon-14 Dating

Given:

Initial Carbon-14 (C-14) in the sample: 0.005 g

Current C-14: 0.002 g

Half-life of C-14: 5,730 years

Steps:

Calculate the fraction of remaining C-14: Divide current C-14 by initial C-14: 0.002 g / 0.005 g = 0.4

Determine the number of half-lives passed: Since 0.4 represents half of the initial C-14, one half-life has passed.

Calculate the sample's age: Multiply the number of half-lives by the half-life: 1 half-life * 5,730 years/half-life = 5,730 years

Therefore, the sample is approximately 5,730 years old.